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Noncommutative vortices and beach waves
G. Cruz
L.R. Juárez
A. A. Minzoni
M. Rosenbaum
IIMAS-FENOMEC, UNAM
Frontiers in Nonlinear Wavesin honor of Vladimir Zakharov's 70th birthday
Pelinovsky, Kevrekidis, Frantzeskikis 2005
Circular vortex
Peierls-Nabarro potential
Static vortex
Peierls-Nabarro potential
Noncommutative NLS equation
Strominger 2000.
Lindstrom-Rocek 2003
Modulation equations
The last expression is the equation of motion for the peak of the vortex, analogous to a particle in a Peierls-Nabarro potential.
Large vortex with low energy
The vortex moves in the lattice generated by the *-product.
The fixed points are the equilibrium positions